Add Fractions


Several examples with detailed solutions and exercises with answers on addition of fractions, are presented.

fraction 1 is used here to denote the fraction of a over b. a is called the numerator and b is called the denominator and must be non zero.

Examples of fractions: fraction 2

NOTE: fraction 3 is undefined since division by zero is undefined in mathematics.

A calculator to add fractions is included in this website. You may use it to check your answers.


How to add fractions?

1. Add fractions with equal denominator

Example 1: Add and simplfy.

fraction 4
Solution to Example 1

To add fractions with the same denominator, you add the numerators, keep the same denominator and simplify if possible

fraction 5


Example 2: Add, simplify and express the final answer as a fraction.

fraction 6
Solution to Example 2

Add the numerators

fraction 7

2. Add fractions with non equal denominators


Example 3: Add, simplify and express the final answer as a fraction.

fraction 8
Solution to Example 3

We first need to find the lowest common multiple (LCM) of the denominators 9 and 6 by factoring into prime factors.
fraction 9
We next convert the two given fractions so that they have common denominator equal to the LCM = 18. The denominator of the fraction fraction 10 is 9 and we need to multiply numerator and denominator by 2 in order to change the denominator to 18

fraction 11

The denominator of the fraction fraction 12 is 6 and we need to multiply numerator and denominator by 3 in order to change the denominator to 18

fraction 13

Now that we have converted the two fractions so that they have common denominator, we can easily add them as follows

fraction 14


Example 4: Add, simplify and express the final answer as a fraction and as a mixed number.

fraction 15
Solution to Example 4

Find the LCM of the denominators 15 and 55

fraction 16

We convert the given fractions so the they have common denominator equal to the LCM = 165. The denominator of the fraction fraction 17 is 15 and both numerator and denominator need to be multiplied by 11 in order to change the denominator to 165

fraction 18

The second fraction fraction 19 is converted to one with the denominator equal to 165 by multiplying numerator and denominator by 3 in order to change the denominator to 165

fraction 20

We now add the fractions

fraction 21


Example 5: Add, simplify and express the final answer as a fraction.

fraction 22
Solution to Example 5

We first convert 2 into a fraction

fraction 23

The common denominator will be 5

fraction 24

We now add

fraction 25


Exercises: Add, simplify and express the answer as a fraction and as a mixed number.
fraction 26

Answers to Above Exercises:.
fraction 27

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